Inconsistency between the Boltzmann distribution for relativistic free particles and the Rayleigh-Jeans law for thermal radiation within classical electrodynamics

Abstract

The classical electrodynamic model introduced by Einstein and Hopf of a massive free particle containing an electric dipole oscillator in interaction with random classical radiation is extended to relativistic particle velocities. The equilibrium distribution of classical particle velocities enforced by the Rayleigh-Jeans law of thermal radiation is found to be different from the Boltzmann distribution for relativistic free particles at the same temperature. Thus apparently there is an inconsistency within classical theory between the relativistic Boltzmann particle distribution and the Rayleigh-Jeans law for thermal radiation.